{"id":"https://openalex.org/W1985081973","doi":"https://doi.org/10.1137/s0036142900375712","title":"Spherical Product Algorithms and the Integration of Smooth Functions with One Singular Point","display_name":"Spherical Product Algorithms and the Integration of Smooth Functions with One Singular Point","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W1985081973","doi":"https://doi.org/10.1137/s0036142900375712","mag":"1985081973"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142900375712","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142900375712","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012279560","display_name":"Ronald Cools","orcid":"https://orcid.org/0000-0002-5567-5836"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ronald Cools","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5031973559","display_name":"Erich Novak","orcid":"https://orcid.org/0000-0002-8341-916X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Erich Novak","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5012279560"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5831,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.65827721,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"39","issue":"4","first_page":"1132","last_page":"1145"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8245301246643066},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6387588977813721},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5937551259994507},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5696181654930115},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.5597220659255981},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5297542214393616},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.47520360350608826},{"id":"https://openalex.org/keywords/gauss","display_name":"Gauss","score":0.4733419716358185},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.46397146582603455},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3680139183998108},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19258397817611694},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11553451418876648}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8245301246643066},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6387588977813721},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5937551259994507},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5696181654930115},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.5597220659255981},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5297542214393616},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.47520360350608826},{"id":"https://openalex.org/C161794534","wikidata":"https://www.wikidata.org/wiki/Q177493","display_name":"Gauss","level":2,"score":0.4733419716358185},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.46397146582603455},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3680139183998108},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19258397817611694},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11553451418876648},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036142900375712","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142900375712","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Decent work and economic growth","score":0.4300000071525574,"id":"https://metadata.un.org/sdg/8"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1566710167","https://openalex.org/W2010722609","https://openalex.org/W2057055143","https://openalex.org/W2073732659","https://openalex.org/W2075245861","https://openalex.org/W2085614905"],"related_works":["https://openalex.org/W2351083540","https://openalex.org/W2953854768","https://openalex.org/W2389690162","https://openalex.org/W2039467239","https://openalex.org/W4231686530","https://openalex.org/W2060497234","https://openalex.org/W3185647786","https://openalex.org/W2317230014","https://openalex.org/W1964609492","https://openalex.org/W103142895"],"abstract_inverted_index":{"We":[0,17,33,66],"consider":[1],"the":[2,25,46,61,85],"problem":[3],"of":[4,28,37,77,100],"numerical":[5],"integration":[6],"for":[7,31,54],"multivariate":[8],"functions":[9,56],"with":[10,39,73,96],"respect":[11],"to":[12],"a":[13,40,51,97],"radial":[14],"symmetric":[15],"weight.":[16],"prove":[18],"that":[19,42,60],"suitable":[20],"spherical":[21,70,92],"product":[22,71,93],"algorithms":[23,49,72],"have":[24,50],"optimal":[26,75],"rate":[27,76],"convergence":[29,78],"n-k/d":[30,79],"Ck-functions.":[32],"also":[34,80],"study":[35],"classes":[36],"integrands":[38],"singularity":[41],"are":[43],"Ck":[44],"outside":[45],"origin.":[47],"Standard":[48],"high":[52],"cost":[53],"such":[55],"because":[57],"they":[58],"require":[59],"function":[62],"is":[63],"smooth":[64],"everywhere.":[65],"construct":[67],"suitably":[68],"modified":[69,91],"an":[74],"in":[81],"this":[82],"case.":[83],"In":[84],"compact":[86],"case,":[87],"we":[88],"can":[89],"use":[90],"Gauss":[94],"formulas":[95],"nonalgebraic":[98],"degree":[99],"precision.":[101]},"counts_by_year":[{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}